Shape-Preserving Interpolation and Smoothing for Options Market Implied Volatility

被引:0
作者
H. Yin
Y. Wang
L. Qi
机构
[1] Minnesota State University Mankato,Department of Mathematics and Statistics
[2] Graduate University of Chinese Academy of Sciences,CAS Research Center of Fictitious Economy and Data Science
[3] Peking University,Guanghua School of Management
[4] Hong Kong Polytechnic University,Department of Applied Mathematics
来源
Journal of Optimization Theory and Applications | 2009年 / 142卷
关键词
Option price function; Risk-neutral density; Implied volatility; Shape-preserving interpolation; Nonparametric estimation;
D O I
暂无
中图分类号
学科分类号
摘要
The interpolation of the market implied volatility function from several observations of option prices is often required in financial practice and empirical study. However, the results from existing interpolation methods may not satisfy the property that the European call option price function is monotonically decreasing and convex with respect to the strike price. In this paper, a modified convex interpolation method (with and without smoothing) is developed to approximate the option price function while explicitly incorporating the shape restrictions. The method is optimal for minimizing the distance between the implied risk-neutral density function and a prior density function, which allows us to benefit from nonparametric methodology and empirical experience. Numerical performance shows that the method is accurate and robust. Whether or not the sample satisfies the convexity and decreasing constraints, the method always works.
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页码:243 / 266
页数:23
相关论文
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